This study proposes the Quadruple Exponentially Weighted Moving Average (QEWMA) control chart, a novel monitoring scheme designed to enhance the detection of small-to-moderate process mean shifts in the presence of autocorrelation. While traditional EWMA-based charts often struggle with dependent data, the proposed QEWMA utilizes a four-layered smoothing mechanism to effectively filter noise in Moving Average processes. The performance of the QEWMA chart was rigorously evaluated using the Numerical Integral Equation (NIE) approach to calculate the Average Run Length (ARL) and the Standard Deviation of Run Length (SDRL). Comparative results across MA(1), MA(2), and MA(3) models demonstrate that the QEWMA chart significantly outperforms the standard EWMA, DEWMA, and TEWMA charts, particularly for subtle shifts (δ≤0.10). The practical utility of the proposed chart was further validated through two real-world applications: monitoring Thailand’s daily median income (MA(3)) and gold futures prices (MA(2)). In both applications, the QEWMA chart exhibited superior sensitivity and faster detection rates, providing more reliable signals for economic and financial surveillance. These findings suggest that the QEWMA chart is a robust and highly efficient tool for quality control in complex, autocorrelated industrial and economic environments.
Neammai et al. (Mon,) studied this question.